# Formation of Vacancies in Si- and Ge-based Clathrates: Role of Electron Localization and Symmetry Breaking

## TL;DR

This study investigates how vacancies form in Si- and Ge-based clathrates, highlighting the influence of electron localization and symmetry breaking, with implications for their structural stability and electronic properties.

## Contribution

It reveals the contrasting stability of vacancies in Si and Ge clathrates driven by electron localization and orbital relaxation effects, using density-functional theory.

## Key findings

- Vacancies are unstable in Si clathrates.
- Up to three vacancies can be stabilized in Ge clathrates.
- Electron localization differences drive the contrasting behaviors.

## Abstract

The formation of framework vacancies in Si- and Ge-based type-I clathrates is studied as function of filling the cages with K and Ba atoms using density-functional theory. Our analysis reveals the relevance of structural disorder, geometric relaxation, electronic saturation, as well as vibrational and configurational entropy. In the Si clathrates we find that vacancies are unstable, but very differently, in Ge clathrates up to three vacancies per unit cell can be stabilized. This contrasting behavior is largely driven by the different energy gain on populating the electronic vacancy states, which originates from the different degree of localization of the valence orbitals of Si and Ge. This also actuates a qualitatively different atomic relaxation of the framework.